International Journal of Renewable Energy Development

The classic Savonius semi-circular blade turbine has a relatively low power coefficient. The performance of a Savonius wind turbine depends on its geometrical parameters. Various blade profiles have been developed in the past years to improve the performance of this class of turbine. In this paper, a new blade shapes of Savonius wind turbine is investigated numerically by using the CFD method , by using transient conditions and set k omega turbulence model.The new blade has different concave and convex shape, which is a combination of the conventional and the elliptical blade. A comparative study of three blade profiles, semi-circular, elliptical and the composed blades have been performed. Flow structures around the rotor have also been analyzed. The results show that changing the blade shape has an effect on the performance efficiency of the Savonius turbine. The new modified and the elliptical blade exhibit higher performance compared to the conventional Savonius wind turbine. The new modified Savonius blade and the elliptical blade exhibit an improved performance compared to the conventional model in the order of 20.5% and 18.2% respectively at the tip speed ratio of 0.8.


Introduction
The development of technologies based on renewable energy is seen as a solution to meet the growing demand for energy and to limit the impact of global warming. Among the most promising renewable energies sources, wind energy appears as clean source of energy available in the form of kinetic energy from the air.
Based on the axis of rotation, wind turbines are divided mainly among horizontal axis (HAWT) and vertical axis (VAWT) wind turbines (Roy & Saha, 2013a). Savonius rotor was designed by the Finnish Engineer S.J. Savonius in 1931(Savonius, 1931 with a basic configuration of an "S-shaped" cross-section or a derived configuration composed of two superimposed semi-circular blades. The operating principle is based on the difference of aerodynamic forces. The simple structure of the Savonius rotor allows operation under winds of all directions, resulting in good starting characteristics. The savonius rotor has gained popularity for ventilators and pumping applications, however, due to its low aerodynamic efficiency, the turbine hasn't been used for power generation (Kamoji et al., 2008). Conventional Savonius rotors have an average performance which is characterized by a lower power coefficient. For this reason, the Savonuis rotor has attracted the attention of researchers in order to improve its performance. Many investigations attempt to improve turbine performance by optimizing geometry parameters such as aspect ratio, turbine buckets, end plates. Research into the effect of aspect ratio and overlap ratio on the Savonius rotor shows that the high performance is obtained when the height of the rotor is twice the rotor diameter (Ushiyama & Nagai, 1988), (Fujisawa & Gotoh, 1992) and for an overlap ratio in the range between 0.15-0.25 (Akwa et al., 2012;Jian et al., 2012;Mojola, 1985;Roy et al., 2014) .The influence of the number of blades has also been studied by many researcher (Blackwell et al., 1977), (Mahmoud et al., 2012). These studies have shown that the performance of the wind rotor decreases as the number of blades increases. To optimize the orientation of the air flow around the blades many augmentation technique have been added such as the shields (Morcos et al., 1981, Alexander & Holownia, (1978, deflector , Youssef et al., 2020, conveyor/deflector (Tartuferi et al., 2015), curtains (Altan & Atılgan, 2010), venting blade (Alom & Saha, 2018), deflector longitudinal (Salleh et al., 2020), V-shaped deflector (Shaughnessy & Probert, 1992), guide vane (El-Askary et al., 2015), straight deflector (Mohamed et al., 2010), they show a considerable improvement in the power of the Savonius wind turbine. The use of a straight deflector resulted in an increase in power coefficient of 27%. The results of developing an optimal shielding configuration show that the peak power coefficient was increased from 0.22 to 0.34. In recent years, severals investigations have been conducted on different blade shapes to improve the performance of the Savonius rotor. In this context Zemamou et al  have introduced a novel blade design based on polynomial Bezier curves and reached a pic value of Cp of about 0.35 at TSR=1.
Zemamou et al (Zemamou et al., 2019) have developed a modified design based on elliptical shape with a straight trailing edge the modified design shows a maximum Cp of 0.335, whereas the conventional model indicates the highest Cp of 0.25. the utilization of the elliptical blades in multi-stage systems has been studied by Mrigua et al. (Mrigua et al., 2020). It is found that the two stages rotor has a higher power coefficient than the single and three stage rotors. Kamoji. (Kamoji et al., 2009a) has carried out an investigation on the Bach-profile rotor without the central shaft. Their result shows that the maximum Cp obtained is 0.21 at Re= 1.510 5 . The disadvantage of a conventional Savonius turbine is the low power and torque coefficient, which is a significant obstacle to the application of Savonius wind turbines (Abdelaziz et al., 2022), (He, 2017).
In order to surmount this problem, some studies have already been conducted, optimizing the geometric parameters of the blades (Sheldahl et al., 1978) (Kacprzak et al., 2013) (Akwa et al., 2012) (Afroz et al., 2012), (Sobczak, 2018), and (Chen et al., 2022). This results in a slight increase in the efficiency of the rotor.
Other researchers have studied and analyzed some additional devices or obstacles ( Fig.1.d and 1c ), to improve the performance of Savonius wind turbines, which leads to a significant increase. However, this modification will increase the complexity of the rotor construction and potentially reduce the starting capacity  (Kalluvila & Sreejith, 2018), (c) obstacle shielding returning blade (Mohamed et al., 2011), (d) SR3345 airfoil SR5050 airfoil and Conveyor-deflector curtain (Tartuferi et al., 2015) (e) Semicircular, Elliptique and Bach shapes.
From an aerodynamic point of view, the wind blowing on the Savonius rotor blades creates a lift force and a drag force. The problem of minimizing the performance of the wind turbine is related to the negative drag force produced by the returning blade that pushes the rotor in the opposite direction of rotation, which requires a change in profile. The developed design in this paper has a concave part of the with straight part and another part with a higher curvature than the semicircular profile which causes the increase of the drag on the concave surface, has an impact on the overall net torque of the turbine. In addition, the straight part of the blades also acts positively and accelerates the rotor moment.

Methodology
The objective of this paper is to present a new composed design of blade based on different combination of conventional and elliptical blades. The new blade has a different concave and convex shape, which is a combination of the conventional blade representing the convex side and the elliptical blade representing the concave side. The rotation mechanism of the Savonius turbine is mainly affected by the increase in concave drag, which affects the overall net torque of the turbine.
The new blade is flatter and thicker than the conventional blade. As the elliptical profile has an almost straight part and another part with a higher curvature than the conventional profile, they mainly cause a difference in pressure drag.
The conventional, elliptical and the new developed Savonius wind turbine are depicted in figure below (Fig. 2). To assess the performance of the investigated designs, the CFD modeling technique is used. The shear stress transport (SST) k-ω turbulence model is employed to simulate the flow field around these turbines. The published experimental results by A. Sanusi (Sanusi et al., 2016) are used to validate the performed model. A comparative study of three blade profiles, semi-circular, elliptical and composed blades have been performed. Finally, this paper provides an analysis of the flow field including velocity and, pressure distribution

Computational domain
In the present study, the Fluent software was used to model the flow around the Savonius rotors. The twodimensional computational domain and the boundary conditions are shown in Figure 3.
The computational domain has two parts separated by a sliding interface: a rotate domain (circular zone) and a fix domain (rectangular zone), the dimension of the computational domain is 10D×15D. The Savonius rotors, is located at the center of the rotate domain, placed at a distance 5D from the top and bottom sides of the rectangular domain, and at a 5D distance upwind, where the condition of inlet velocity was assigned.

Mathematical Model
This paragraph discusses the mathematical equations that are used in the modeling. These equations combine the different flow parameters. For an incompressible flow, the equations governing the conservation of the mass and the momentum are given respectively by: Where = , ui, p, xi and t are respectively, the kinematic viscosity, the flow velocity, pressure, and spatial and temporal coordinates. The numerical solution uses the notion of average variables. It is therefore necessary to transform the NS equations into averaged equations according to the Reynolds decomposition. Reynolds' method consists of decomposing each physical variable into an average and a fluctuating value: The equations governing the conservation of the mass and momentum are (averaged by Reynolds' procedure) given respectively by: • Continuity equation: Where − ′ ′ is the Reynolds stress tensor (Celik, 1999). This requires additional modelling to close the RANS equations which leads to the creation of different turbulence models such as the S-A model, the k-Ɛ model and the k-ω model. The Boussinesq hypothesis is used to solve the Reynolds stresses. Equation is expressed as follow: Where = 1 2 ′ ′ , and ≈ √ . represent respectively the Turbulence kinetic energy and the eddy viscosity. Here l is the turbulent length scale.

Turbulence Model
In this study, the SST k-ω turbulence model (Menter, 1994) has been utilized, due to its efficiency and better prediction (Ferdoues et al., 2017). The SST k-ω is a combination between two models, the turbulence model k-ε and the model of turbulence k-ω (Song et al., 2015;Mishra et al., 2019). The SST k-ω model has two partial equations where 'k' is the turbulence kinetic energy and ω mention to a specific dissipation.

Performance parameter
Considering the solution of conservation equations and the chosen turbulence model, the torque of rotor (T) can be calculated by integrating the force difference resulting from the shear and the pressure on the rotor as shown below (Nasef et al., 2013): where Fi pressure and Fi shear are the pressure and shear forces vectors acting on the face area vector Ai respectively and d is a local torque arm vector from the rotation axis, about which the moment is taken. where p and τ are the pressure and shear stress, respectively. The Coefficient of Torque CT, Coefficient of Power CP and Coefficient of Static Torque are given respectively from the following equations (Mahmud et al., 2018). Static torque is the net torque of the rotor in the Static state. Which is principally responsible for the starting capacity of the rotor (Roy & Saha, 2013b).

Meshing and boundary condition
The domain of computational is discretized using unstructured hybrid grids. The mesh must be fine enough to resolve with precision the physics of the flow, in particular at the level of the boundary layer in the vicinity of the rotor surface. For this reason, the inflation meshing technique is applied to the rotors wall, by creating layers of fine mesh in the direction normal to a wall. The first layer thickness takes the value of 5.10 -5 m the growth rate of 1.2 as shown in Figure 4, this value was calculated using the equation 7.
The frictional velocity is calculated from the following equation: Where represents wall shear stress, dy is the distance of first cell from rotors wall and µ= 1,811.10 -5 Ns.m -2 is the dynamic viscosity. Figure 5 shows the y+ variations for all Savonius rotors at rotation angle 90°. In order to capture the flow properties in the vicinity of the blade, a mean y+ value of less than 1 can be observed.
The SIMPLE (Semi-Implicit Method for Pressure Linked Equations) pressure-velocity coupling method was used in all simulations for all the equations, a second order wind spatial discretization algorithm has been used, and a Least Squares Cell Based algorithm has been used for the gradients. Table 2 reports the boundary condition parameters and solver configuration.  Figure 6 shows the CT of the Conventional Savonius rotor in 10 rotation periods are plotted against the rotation angle. It can be seen that after the 3 period, the variation in CT almost follows a periodic variation, and is therefore averaged to give a more precise value.

Grid-independent test
Numerical simulation is carried out over five completed rotations of the turbine. The maximum number of iterations per time step fixed at 50. Absolute criteria are used to monitor the convergence of the solution with a value of 10 -5 ( Table 2). The mesh is one of the most important parameters of the simulation to achieve high accuracy and avoid lack of convergence. The gridindependent test has been carried out by varying the grids between 50,000 and 300,000, the averages Cp of the grids is shown in Figure 7. The simulation results show that there is no significant change in the coefficient of torque beyond 130000 elements

Validation of the numerical methodology
The simulation results of the flow around conventional wind turbine Savonius with two blades, using the SST − turbulence model were compared with the experimental results from (Sanusi et al., 2016) to evaluate the precision the current numerical methodology. The variation of the torque coefficient, of both experimental and numerical approach for different tip speed ratios, are shown in Figure  8.
The maximum error value between the experimental and numerical data about 6.25% at λ=0.2. The pattern variation of both curves show a similar behavior. The computational results have a good accord with the experiment test. As a result, it is suitable to perform the numerical method in order to foresee the performance of Savonius rotors.

Comparison of the geometries conception.
In the present investigation, 2D unsteady simulations is conducted on the semi-circular bladed, elliptical bladed and composed bladed under identical conditions. Figure 9 shows the variations in the power coefficient CP and the torque coefficient CT for the three profiles with the Tip Speed Ratio.  From the analysis, it can be noticed that the rotor speed decreases with the application of load, and therefore the variation of CT decreases when TSR increases, (Figure 9). The composed profile has higher power coefficients over the tested range of TSR compared to elliptical and conventional profiles. The composed blade shows a CP peak of 0.34 at TSR=0.80, whereas at the similar TSR, the CP peak is 0.33 and 0.27 for the elliptical and the semicircular profiles, respectively. The simulation thus exhibits an improvement of CP in the composed profile compared to the semicircular profiles by 20.5%. The coefficient of power decreases for all blade models beyond TSR = 0.8. It is believed that the power coefficients of elliptical and conventional profiles are reduced due to the formation of vortices downstream of the return blades. The coefficient of torque as a function of time at tip speed ratio 0.8 is shown in Figure 10. It can be noted that the values of torque coefficient the composed-blade are greater over the conventional-blade rotor. Concentrate on the last revolution of simulation, a comparison of the moment coefficient versus rotor angle for the two rotor types is shown in Figure 11. The curves of the instantaneous torque coefficient of the two rotors show a similar trend within one rotation period. The instantaneous torque coefficient is covered by two cycles in one revolution. The torque values of the composed blade rotor are generally higher than the conventional blade rotor, except for rotor angles between [75°-105°] and [255°-285°]. The maximum value of torque for the composed blade rotor occurs at rotor angles of 22° and 202°, and it is about 20.5% higher compared to the conventional blade rotor at rotor angles of 25° and 205°. The ability to accept wind from various directions is similar for the combination blade rotor and the conventional blade rotor. The composed blade rotor exhibits an increase in the torque coefficient resulting in an improvement in the power coefficient.

Pressure and velocity contours
The contours of the pressure of three rotor profiles are shown in Figure 12. It is clearly observed that the pressure in the composed profile is of the order of 20-40 N/m 2 , whears in the other profiles the pressure found to be lesser.
On the concave side of the returning blade, the pressure for the composed profile is higher than the other ones. The pressure on the concave face of the blade can contribute to the increase of the positive torque, while the convex face has the possibility to reduce the rotor torque. In addition, the higher pressure zone on the convex side of the returning blade of the composed profile is lower than the other ones, the resulting torque is therefore higher in the composed profile. In addition, the effect of overlapping flows is more prominent for composed blades, which reduces the negative torque (Kacprzak et al., 2013). whereas, the effect of overlapping flow and a better pressure field on the concave side of the returning blade is more substantial, in the composed blade as compared to other ones. The pressure contours for composed blade are similar to Saeed et al., (2019). The amplitude of the velocity near the surface of the advancing profile is around 1.5 to 4 m.s -1 , 2.5 to 4 m.s -1 and 3.5 to 5 m.s -1 for semicircular, elliptic and composed blades respectively. The magnitude of velocity in the convex side of the returning blade is lower in the composed blade than the others ones. It is observed that the flow gets accelerated near the tip of the blades, the high velocity zone is relatively closer to the surface of the composed blade than that of the others profiles, and it can also be seen that the tip losses are greater in the semi-circular and elliptic blades than in the composed blade. An overlapping jet, is formed on the concave face of the advancing blade and reaches the retuning blade. The overlapping is found to be more prominent in the composed blade 5-6.5 m/s than the semicircular blade 3-4.5 m/s and elliptic blade 3.5-5 m/s. The increase in speed in this area suggests that the negative contribution of the returning blade to the overall torque is considerably reduced. The formation of wake on the concave side of returning blade of composed profile is found to be smaller than the semicircular and elliptical profiles

Effect of number Reynolds
The study of a vertical axis wind turbine subjected to operating conditions in the presence o f wind is very complex, because the wind has an instantaneous variation in speed and direction. The wind velocity is adjusted corresponding to a given Reynolds number = . Both conventional and composed wind turbines are tested at different Reynolds numbers corresponding to wind speeds of 3.2 m.s -1 , 4.2 m.s -1 , 6.2 m.s -1 and 7.2 m.s -1 . Figure 14 shows the variation of power coefficient at different Reynolds numbers. These curves have similar trends for the power coefficients of all rotors. The maximum Cp values were found for all rotors at a TSR of 0.8. The power coefficient increase as a function of the Reynolds number. (Kamoji et al., 2009b). The maximum coefficient of power increases with the increase in the Reynolds number. This increase in Cpmax with increased Reynolds number has also been noted by Sheldahl (Sheldahl et al., 1978) for conventional Savonius rotors. Reynolds number plays a very major role in the aerodynamic performance.  Figure 15 shows the pressure contours of the composed and the semicircular profiles as a function of the rotor angle. At 15°, on the concave side of both blades seems to have high pressure. the pressure distribution for all rotors tested is almost the same, but the suction area and pressure amplitude for composed blades is larger than that of the conventional blades. Consequently, in the rotor with alpha 15° blades, the pressure difference for composed blade causes additional force, and in results, an improvement in performance. It is clear from the contours, that there is a strong fluctuation in pressures resulting in high turbulence behind the conventional blade rotor.
At α=60° the first one being a low-pressure zone near the tip at 60° and the second one being a high-pressure zone bon the mid of the convex surface of the blade at 240°. The returning blade of conventional profiles, a highpressure zone appears on the convex side, and a lowpressure zone appears on the concave side compared to composed profiles. The pressure differential provides a high torque that prevents the turbine from rotating. At 150°, a great low-pressure vortex leaves the top of the advancing blade. It is observed that such pressure difference is higher in the composed profile than the semicircular profile. This results in a higher Cp in the composed profile.

Self-starting
Finally, in order to verify the ability of the improved system to self-start, the static torque coefficient was calculated for both conventional and composed blades at different rotor angles. Figures 16 gives the variation of the static torque coefficient for both rotors as a function of the rotor angle.  It can be seen that the conventional and composed blades show a similar evolution of the static torque coefficient characteristics. The conventional Savonius rotor is a selfstarting rotor, this feature is retained for the composed blade rotor. To highlight the results achieved, a comparison with the findings of other investigators involved in the development of the Savonius wind turbine blades is presented in the table below. It can be observed that the power coefficient found in this study is higher than the power coefficients derived from previous investigations.

Conclusion
The Savonius rotor is a small-scale wind power system, but it suffering from low efficiency. Therefore, the main objective of this study is to develop an improved design, which produces higher performance. In this work, we present a new form of Savonius wind turbine blade combining two different sides. The convex part has the semicircular shape of the conventional blade. The concave part is elliptical. The aerodynamic performances of these Savonius rotors are studied using CFD. 2D unsteady simulations using the SST k-ω turbulence model are conducted for the composed, Elliptical and Semicircular profiles at a wind speed of 6.2 m.s -1 . Moreover, to confirm the accuracy of the computational results, a validation of the simulation results against experimental data is performed. The results of the simulation around the conventional blade of the Savonius rotor show good agreement with experimental data. The composed blade wind turbine has a Cpmax =0.34, whereas that of the conventional SSWT is 0.27, this means that a performance improvement of 20.5% is achieved with the composed blades over the conventional blade profile at the tip speed ratio of 0.8. Regarding the Reynolds number effect on the performance of the savonius rotor, the results confirm that the composed blade has a better performance than the conventional blade at different Reynolds numbers. Thus, the new modified Savonius wind turbines have significantly better self-start than the conventional design. In this study we have developed a compound blade to be used as a new model of the savonius rotor, for future studies we could consider using this model in multistage rotors to increase the power output.